Option C: The line is the line of reflection.
Explanation:
It is given that the across a line, and
Thus, the reflection is given by ⇒
Now, we shall determine the line of reflection.
Option A: the x-axis
To reflect the coordinates across x-axis is given by ⇒
Thus, the line of reflection of the coordinate L across x-axis is given by
⇒
This is not the equal to the given line of reflection ⇒
Hence, the line of reflection is not across x-axis.
Thus, Option A is not the correct answer.
Option B : the y-axis
To reflect the coordinates across x-axis is given by ⇒
Thus, the line of reflection of the coordinate L across y-axis is given by
⇒
This is not the equal to the given line of reflection ⇒
Hence, the given line of reflection is not across y-axis.
Thus, Option B is not the correct answer.
Option C: the line
To reflect the coordinates across is given by ⇒
Thus, the line of reflection of the coordinate L across the line is given by ⇒
This is equal to the given line of reflection ⇒
Hence, the given line of reflection is across the line
Thus, Option C is the correct answer.
Option D : the line
To reflect the coordinates across is given by ⇒
Thus, the line of reflection of the coordinate L across the line is given by ⇒
This is not the equal to the given line of reflection ⇒
Hence, the given line of reflection is not across the line .
Thus, Option D is not the correct answer.